1. Field of the Invention
The invention relates to system exhibiting complex dynamic and chaotic motion for use as laboratory experiments, demonstrations, and education. The invention also relates to linear motors and their application in such systems.
2. Description of the Prior Art
Dynamical systems theory has become an important analytical method for understanding random vibrations, fluid motion, ecology, and many other systems modeled by ordinary differential equations. A number of systems have become key examples in education and research and are discussed in popular textbooks (see for example Guckenheimer and Holmes, 1993). One such example is the bouncing ball on a vibrating table. A wonderful aspect of the bouncing ball system is that the equations of motion are simple, but the motion itself exhibits amazing complexity such as chaos (see Vincent, 1997). Classroom discussions consider an idealized system where the ball remains fixed in the horizontal direction bouncing perfectly up and down. In practice, however, small imperfections in the table and the ball cause the ball to drift off the table. No practical demonstration system for bouncing ball dynamics has been reduced to practice in the prior art.
Several prior art devices address related problems, put to not meet the objectives of the current invention.
In U.S. Pat. No. 3,882,736 issued to Jayne, an apparatus is disclosed for maintaining a bouncing ball between concave plates. The motion of the ball in this system is not the same as the motion of a ball on a vibrating table however.
In U.S. Pat. No. 5,028,053 issued to Leopold, a ball having twenty-two hemispherical projections is disclosed. The invention does exhibit complex bouncing behavior, but the bouncing does not have the motion of a bouncing ball on a vibrating table.
It is clear from the discussion above that there is no device capable of demonstrating the dynamics of a ball bouncing on a vibrating table. Accordingly, it is desirable to provide for a new bouncing ball apparatus, which is simple, reliable, and produces ball motions consistent with mathematical models of a bouncing ball on a vibrating table. Further what is needed is a device that constrains the ball motion to a simple vertical up and down motion and that can produce rapid vibrations of an impacting surface below the ball.
It is the principle object of this invention to provide a system for demonstrating nonlinear dynamics and chaotic motion. More specifically, the objects of this invention are: to demonstrate the dynamics of a bouncing ball on a vibrating piston and to provide the user with accurate measurements of the piston height and the time that the ball contacts the piston. Further objects of this invention are to minimize cost, and create motions that which largely follow the simple equations of motion as described in Guckenheimer and Holmes, 1993.
The present invention is directed at a linear motor driven bouncing ball system. By nature of its novel component configuration manufacturing costs are minimized, and the alignment of the piston with the ball is excellent. Further the time that the ball impacts the piston is measured accurately and inexpensively with a novel sensor choice and placement. Likewise the piston height is measured with a novel sensor choice and placement.
The mechanism allowing for the relative motion of the ball and piston is novel, low-cost, and precise in the sense that friction on the ball is minimized, and the motion of the piston is sensed so that its motion can be precisely controlled by feedback.